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Strichartz estimates for non‐degenerate Schrödinger equations
Author(s) -
Taira Kouichi
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800148
Subject(s) - mathematics , degenerate energy levels , euclidean space , metric (unit) , schrödinger equation , euclidean geometry , space (punctuation) , mathematical analysis , contrast (vision) , mathematical physics , physics , geometry , quantum mechanics , linguistics , operations management , philosophy , optics , economics
We consider the Schrödinger equation with a non‐degenerate metric on the Euclidean space. We study local in time Strichartz estimates for the Schrödinger equation without loss of derivatives including the endpoint case. In contrast to the Riemannian metric case, we need the additional assumptions for the well‐posedness of our Schrödinger equation and for proving Strichartz estimates without loss.